Nest complementary objects quick, without having to deform,distort?
To construct the dual object, you can:


X Delete > 'Faces Only' of the original
F between selected vertices to create new edges
F selected edges to create new faces




If you already have the complementary objects, not in the right orientation or scale, maybe this answer will help?

EDIT: following commentary .. this sequence was keyed manually, forward and in reverse from a static exact fit position. I personally think 'cheating' is the easiest approach.